The treatise on pp. 52-65 is the only one in English known on the subject. It describes a method of calculation which, with slight modifications, is current in Russia, China, and Japan, to-day, though it went out of use in Western Europe by the seventeenth century. In Germany the method is called “Algorithmus Linealis,” and there are several editions of a tract under this name (with a diagram of the counting board), printed at Leipsic at the end of the fifteenth century and the beginning of the sixteenth. They give the nine rules, but “Capitulum de radicum extractione ad algoritmum integrorum reservato, cujus species per ciffrales figuras ostenduntur ubi ad plenum de hac tractabitur.” The invention of the art is there attributed to Appulegius the philosopher. The advantage of the counting board, whether permanent or constructed by chalking parallel lines on a table, as shown in some sixteenth-century woodcuts, is that only five counters are needed to indicate the number nine, counters on the lines representing units, and those in the spaces above representing five times those on the line below. The Russian abacus, the “tchatui” or “stchota” has ten beads on the line; the Chinese and Japanese “Swanpan” economises by dividing the line into two parts, the beads on one side representing five times the value of those on the other. The “Swanpan” has usually many more lines than the “stchota,” allowing for more extended calculations, see Tylor, _Anthropology_ (1892), p. 314. Record’s treatise also mentions another method of counter notation (p. 64) “merchants’ casting” and “auditors’ casting.” These were adapted for the usual English method of reckoning numbers up to 200 by scores. This method seems to have been used in the Exchequer. A counting board for merchants’ use is printed by Halliwell in _Rara Mathematica_ (p. 72) from Sloane MS. 213, and two others are figured in Egerton 2622 f. 82 and f. 83. The latter is said to be “novus modus computandi secundum inventionem Magistri Thome Thorleby,” and is in principle, the same as the “Swanpan.” The Exchequer table is described in the _Dialogus de Scaccario_ (Oxford, 1902), p. 38. +The Earliest Arithmetics in English.+ +The Crafte of Nombrynge+ _Egerton 2622._ [*leaf 136a] Hec algorism{us} ars p{re}sens dicit{ur}; in qua Talib{us} indor{um} fruim{ur} bis qui{n}q{ue} figuris. [Sidenote: A derivation of Algorism. Another derivation of the word.]